Evaluate the following integrals.int_0^{pi/2}4^{sin x}cos xdx

Question

Evaluate the following integrals.
$\int_{0}^{\frac{π}{2}} 4^{\sin x} \cos x d x$

Answer 1

$Integration$
$\int_{0}^{\frac{π}{2}} 4^{\sin x} \cos x d x$
$Let us take a substitution$
$\sin x = z$
$\cos x d x = d z$
$\int_{0}^{1} 4^{z} d z$
$= [\frac{4^{z}}{\ln 4}]_{0}^{1} = \frac{4}{\ln 4} - \frac{1}{\ln 4}$
$= \frac{3}{\ln 4}$
$This is the required answer.$

Evaluate the following integrals.int_0^{pi/2}4^{sin x}cos xdx

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